Question

Amit is three years elder to his sister five years ago, three fifths of his age was equal to three fourths of her age. How old are Amit and his sister how?

Answer 1

Amit's present age $=x$ and $5$ years ago age is $x-5$

Sisiter's present age = $y$ and $5$ years ago - $y-5$

given $x-5=(y-5)+3$.....(i)

$\Rightarrow x-y=3$

and $\frac{3}{5}x=\frac{3}{4}y$.....(ii)

$12x=15y$

$12x-15y=0$

$\therefore$ $4x-5y=0$.....(iii)

equation $\left(1\right)\times 4$

$\therefore$ $4x-4y=12$.....(iv)

Equation $\left(iii\right)$ $-$ equation $\left(iv\right)$ we get

$y=12$

$\therefore$ $x=15$

$\therefore$ their present ages Amit $=15$

His sister $=12$